An efficient method for calculating the pair distribution functions of a ternary hard-sphere system inrspace within the Percus-Yevick approximation

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Abstract
We present a direct method which allows an accurate and—at the same time—economical calculation of the pair distribution functions (PDFs) gij (r) of an additive ternary hard-sphere system within the Percus—Yevick approximation. The approach is based on the fact that for this approximation the Laplace transforms [ĝij (s)] of the PDFs are known analytically, so that the inversion of the ĝij (s) into r space can be performed exactly. The expressions presented here allow the determination of the ĝij (r) for r values up to 8R 1, R 1 being the diameter of the smallest species; this range in r space should be sufficient for applications in standard algorithms of liquid state theory, such as thermodynamic perturbation theories or integral-equation approaches.

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